A Supergeometric Faà di Bruno Formula

Abstract: We extend the multivariate Fa`{a} di Bruno formula to the super case, where anticommuting odd coordinates are considered. The formula takes the same form as the classical case but contains some nontrivial signs, which essentially measure the failure to order the odd factors and derivatives optimally. As a quick application, we obtain an explicit combinatorial formula for the generalized super Bell polynomials, defined by Fan and Hon.